# Explicit Automorphic Forms for the Rational Function Field, and Their Galois Representations

 MEMBERS SEMINAR Topic: Explicit Automorphic Forms for the Rational Function Field, and Their Galois Representations Speaker: Zhiwei Yun Affiliation: Member, School of Mathematics Date: Monday, March 22 Time/Room: 2:00pm - 3:00pm/S-101

In this talk, we will give explicit examples of Langlands correspondence for reductive groups over the rational function field $F=k(t)$ . Fixing appropriate local ramifications, it is sometimes possible to write down explicit Hecke-eigenforms using the combinatorics of the affine Weyl group. Some of these examples give interesting Galois representations, for example, those with Zariski dense image in E_7, E_8, F_4 and G_2 , and hypergeometric local systems. We will see how ideas from geometric Langlands correspondence help understand the more "classical" Langlands correspondence. This is joint work with J. Heinloth and B-C. Ngo.